Brush library in Blender
You don't export anything from Blender to Blender. You simply keep them in a .blend file and append them when you need (File → Append).

However, unused textures are considered as orphan data. In Blender, orphan data are not kept in the .blend file, so they disappear as soon as you close it.

So, in order to force them to stay in your library .blend file, you will have to open the outliner, switch to the orphan data view, and check every data you want to keep. (Those kept have a checkmark, those unkept have an X instead, click the mark to switch between.)